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8/3/2019 Lie Gonzalez Ch2
1/26
CCU, Taiwan
Wen-Nung Lie
Chapter 2 : Digital Image
Fundamentals
8/3/2019 Lie Gonzalez Ch2
2/26
2-1CCU, Taiwan
Wen-Nung Lie
Image formation in the eye
Components : lens, retina Focal length varies (17 ~14 mm) as the refractive
power increases from minimum to maximum or the
focused object locates from far to near
8/3/2019 Lie Gonzalez Ch2
3/26
2-2CCU, Taiwan
Wen-Nung Lie
Human visual perception
Weber ratio Mach bands
Simultaneous contrast Optical illusion
8/3/2019 Lie Gonzalez Ch2
4/262-3CCU, Taiwan
Wen-Nung Lie
Brightness discrimination of
the eye Weber ratio
The ability of the eye to discriminate betweenchanges in light intensity at any specific
adaptation level is different
Weber ratio : , is the increment ofillumination discriminable 50% of the time with
background illuminationI
Small : good brightness discrimination
Large : poor brightness discrimination
I
I
I
I
I
I
I
8/3/2019 Lie Gonzalez Ch2
5/262-4CCU, Taiwan
Wen-Nung Lie
Typical Weber ratio as a
function of intensity
Brightness discrimination is poor at low levels of
illumination
At low levels of illumination, vision is carried out by
activity of rods, at high levels, it is by cones
8/3/2019 Lie Gonzalez Ch2
6/262-5
CCU, Taiwan
Wen-Nung Lie
Simultaneous contrast
A regions perceived brightness does not dependsimply on its intensity
In the figure below, all the center squares have exactly
the same intensity
8/3/2019 Lie Gonzalez Ch2
7/262-6
CCU, Taiwan
Wen-Nung Lie
Optical illusion
The eye fills in nonexisting information or wrongly
perceives geometrical properties of objects
8/3/2019 Lie Gonzalez Ch2
8/262-7
CCU, Taiwan
Wen-Nung Lie
Quantities to describe quality
of chromatic light source
Radiance Total amount of energy that flows from the light
source (Watts, W)
Luminance A measure of the amount of energy an observer
perceives from a light source (lumens, lm)
Brightness A subjective descriptor of light perception
Light emitted from a far infrared source have high radiance,but almost no luminance for a sensor in visible band
8/3/2019 Lie Gonzalez Ch2
9/26
2-8CCU, Taiwan
Wen-Nung Lie
Image sensing & acquisition
The illumination source emits energy which isreflected or absorbed by the element of the scene
being imaged
The wavelength of an EM wave required to see anobject must be of the same size as or smaller than the
object
The physical properties of the sensor materials alsolimits the capability of imaging sensors (cf. CCD &
CMOS, CCD & IRCCD)
8/3/2019 Lie Gonzalez Ch2
10/26
2-9CCU, Taiwan
Wen-Nung Lie
Image scanning architectures
Single sensor
Sensor strip, the motion of stripcompletes the other dimensionsimaging
Need algorithm
8/3/2019 Lie Gonzalez Ch2
11/26
2-10CCU, Taiwan
Wen-Nung Lie
2-D sensor array, up to 4000x4000
noise reduction is achieved by long
integration time
8/3/2019 Lie Gonzalez Ch2
12/26
2-11CCU, Taiwan
Wen-Nung Lie
Image formation model
Intensity=illumination*(reflectance ortransmissivity)
),(),(),( yxryxiyxf =
8/3/2019 Lie Gonzalez Ch2
13/26
2-12CCU, Taiwan
Wen-Nung Lie
Image sampling &
quantization
Digitalizing the coordinate values is calledsampling. Digitalizing the amplitude values is
called quantization
Sampling for 2-D sensor array is needless image content is a consideration in choosing parameters
in sampling and quantization
8/3/2019 Lie Gonzalez Ch2
14/26
2-13CCU, Taiwan
Wen-Nung Lie
Representing digital images Definition of coordinate system
Dynamic range of an image
the range of values spanned by the gray levels of existing pixels
Spatial resolution (e.g., dpi, or 1024x1024)
Gray-level resolution (8 (often visual), 10, 12 (e.g.,
thermal), or 16 bits/sample)
8/3/2019 Lie Gonzalez Ch2
15/26
2-14CCU, Taiwan
Wen-Nung Lie
Different spatial resolution, but with the same display size
8/3/2019 Lie Gonzalez Ch2
16/26
2-15CCU, Taiwan
Wen-Nung Lie
False contouring effect False contouring effect is quite visible in images displayed
using 16 or less gray levels
8/3/2019 Lie Gonzalez Ch2
17/26
2-16CCU, Taiwan
Wen-Nung Lie
Isopreference curve InNkplane (N: spatial resolution, k: graylevel resolution)
Points on the same curve represent equal subjective quality
The isopreference curve tends to shift right and upward
For images with a large amount of detail(e.g., crowd), only a few gray level maybe needed (see the vertical behaviorwhich is graylevel-independent)
8/3/2019 Lie Gonzalez Ch2
18/26
2-17CCU, Taiwan
Wen-Nung Lie
Zooming and shrinking digital
images Zooming : oversampling
shrinking : undersampling
Methods
Nearest neighbor interpolation Pixel replication
Bilinear interpolation
Use more neighbors for interpolation (e.g., cubicinterpolation)
Blur an image slightly before shrinking it (according to
sampling theory)
8/3/2019 Lie Gonzalez Ch2
19/26
8/3/2019 Lie Gonzalez Ch2
20/26
2-19CCU, Taiwan
Wen-Nung Lie
Cubic interpolation)]1,(),()1,()2,([({),( +++++++=+ ykxfykxfykxfykxfdydydyykxh
)])1,(2),(2)2,()1,([ ++++++++ ykxfykxfykxfykxf
2,1,0,1for),()]}1,()1,([ =++++++ kykxfykxfykxf
)],1(),(),1(),2([({),( yxhyxhyxhyxhdxdxdxyxg +++=
)]),1(2),(2),2(),1([ yxhyxhyxhyxh ++++
),()]},1(),1([ yxhyxhyxh +++
xR
xdx =
yR
ydy =
),(),(
=
R
y
R
xyx
By 16 neighborhoods
g(x,y)f x y( $, $)
8/3/2019 Lie Gonzalez Ch2
21/26
2-20CCU, Taiwan
Wen-Nung Lie
Comparisons for zooming
techniques Duplication
Bilinear interpolation
Cubic interpolation
Edge preserving zooming (to be discussed)
4Xzooming
duplicate bilinear cubic
8/3/2019 Lie Gonzalez Ch2
22/26
2-21CCU, Taiwan
Wen-Nung Lie
Image resampling (non-
integer zooming or shrinking) For non-integer zooming or shrinking
Steps :
For each point in G(x,y), compute its non-grid correspondence in
F(x,y) by the ratioR
Obtain the assigned graylevel by bilinear interpolation technique(by using the four nearest neighbors)
ZR
(4,4)(2.7, 2.7)
F(x,y) G(x,y)
R =1.5
8/3/2019 Lie Gonzalez Ch2
23/26
2-22CCU, Taiwan
Wen-Nung Lie
Some basic concepts in DIP
4-neighborhoods and 8-neighborhoods
4, 8-connected
Adjacency
Connected and graylevels are similar (in an allowed set)
4, 8, or m-adjacency (mixed)
Two pixels are not 8-connected if they can bechained together via 4-connected
8/3/2019 Lie Gonzalez Ch2
24/26
2-23CCU, Taiwan
Wen-Nung Lie
Connected component
Any two pixelsp and q in a region S are connected via
4 or 8 neighborhoods in S (exists a path)
Distance measures Euclidean distance
D4 distance (city-block distance)
2:2 yxnorm
=
=N
n
nnyxyxnorm
11
:1tysxqpD +=),(4
2
21012
2
212
212Equal-distance map
8/3/2019 Lie Gonzalez Ch2
25/26
2-24CCU, Taiwan
Wen-Nung Lie
D8 distance (chessboard distance)
Dm distance (the shortest m-path between the points)
depends on the pixels along the path
),max(),(8
tysxqpD =
21112
21012
21112
22222
22222
P1
P4
P2
P3
P
The m-path between p and p4 isdependent on the value (0 or 1) of p1and p3 -- 2 or 3 or 4
nnNn
yxyx == ,1
supTchebyshev (supermum ormaximum) norm
8/3/2019 Lie Gonzalez Ch2
26/26
2-25CCU, Taiwan
Wen-Nung Lie
Linear and nonlinear operation on images
)()()( gnHfaHbgafH +=+